7 citations · 19 across the 17 of their papers we have counts for
18 papers
Fragments of arithmetic and cyclic proofs
Lev D. Beklemishev, Daniyar S. Shamkanov, Ivan N. Smirnov
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing induct…
Automatic structures and the problem of natural well-orderings
Lev D. Beklemishev, Fedor N. Pakhomov
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude…
Periodic frames
Lev D. Beklemishev, Yunsong Wang
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological…
On the unification problem for GLP
Lev D. Beklemishev
We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the for…
Conservativity spectra and generalized Ignatiev model
Lev D. Beklemishev
We study a generalization of the notion of conservativity spectrum of an arithmetical theory to a language with transfinitely many truth definitions. We establish a correspondence…
Axiomatizing Origami planes
Lev Beklemishev, Anna Dmitrieva, Johann A. Makowsky
We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragme…
Reflection algebras and conservation results for theories of iterated truth
Lev D. Beklemishev, Fedor N. Pakhomov
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theo…
Axiomatizing provable -provability
Evgeny Kolmakov, Lev Beklemishev
A formula is called \emph{-provable} in a formal arithmetical theory if is provable in together with all true arithmetical -sentences taken as additional…
A universal Kripke frame for the variable-free fragment of RC
Lev D. Beklemishev
This note characterizes a universal Kripke frame for the variable-free fragment of the reflection calculus with conservativity operators RC. The frame here is obtained fro…
Reflection calculus and conservativity spectra
Lev D. Beklemishev
Strictly positive logics recently attracted attention both in the description logic and in the provability logic communities for their combination of efficiency and sufficient expr…
Notes on a reduction property for GLP-algebras
L. D. Beklemishev
We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is…
Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics
Lev Beklemishev, Daniyar Shamkanov
We study abstract versions of Gödel's second incompleteness theorem and formulate generalizations of Löb's derivability conditions that work for logics weaker than the classical on…
A Many-Sorted Variant of Japaridze's Polymodal Provability Logic
Gerald Berger, Lev D. Beklemishev, Hans Tompits
We consider a many-sorted variant of Japaridze's polymodal provability logic . In this variant, which is denoted , propositional variables are assi…
A note on strictly positive logics and word rewriting systems
Lev D. Beklemishev
We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a…
Positive provability logic for uniform reflection principles
Lev Beklemishev
We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker lan…
Topological interpretations of provability logic
Lev Beklemishev, David Gabelaia
Provability logic concerns the study of modality as provability in formal systems such as Peano arithmetic. Natural, albeit quite surprising, topological interpretation of p…
On provability logics with linearly ordered modalities
Lev D. Beklemishev, David Fernández-Duque, Joost J. Joosten
We introduce the logics GLP(Λ), a generalization of Japaridze's polymodal provability logic GLP(ω) where Λis any linearly ordered set representing a hierarchy of provability operat…
Topological completeness of the provability logic GLP
Lev D. Beklemishev, David Gabelaia
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopologi…